Trisha Daigle
Psy 633: One-sample t-test
Generally, the t-test is used in two contexts:
As a sub for z when some of the info for z is unknown
This is the “one-sample” test – not terribly common, but sometimes useful
As a test for comparing two samples when no population info at all is available
This is the most common version – widely used in all sciences.
Problems with z:
Usually don’t know enough about the population to compute z
Especially a problem regarding standard error
Less versatile than t – i.e., can’t be used in as many different situations
Can be used when µ is known, but σ is not known
Can be used when µ is not known, but can be reasonably estimated or else
arbitrarily established: e.g., as in manufacturing and education, where an
“ideal” mean can be stipulated
Solution: substitute sample std error for pop std error in the z formula
This new formula is the t-test formula
In the single-sample test, one degree of freedom is lost to the sample mean, so the test has n-1 degrees of freedom [df = the # of scores that are free to vary, taking into account the computation of the mean]
As df increases, sample var is better estimator of pop var
also t is better approximation of z (distribution approaches normal)
Weakness of t is that there is more variability in it, thus more chance of making a Type I decision error
Solution is to use as large an n as feasible
In formula,
Numerator reflects: effect of the IV on the DV
[Note that this is one of the major “power” factors]
Denominator reflects:
Individual diff’s, n, unwanted var (“error”)
[Note that all of these are major “power” factors]
The problem for the researcher is to make the numerator as large as possible, within ethical & practical reason, and the denominator as small as possible. Assuming that both of those ends are accomplished, then if there is a diff betw M and µ, the t-test will reveal it.
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